In this, the first of the five major categories of this course, the topics covered include:

Limits of functions (including one-sided limits)
• An intuitive understanding of the limiting process.
• Calculating limits using algebra.
• Estimating limits from graphs or tables of data.

Asymptotic and unbounded behavior
• Understanding asymptotes in terms of graphical behavior.
• Describing asymptotic behavior in terms of limits involving infinity.
• Comparing relative magnitudes of functions and their rates of change (for example,
contrasting exponential growth, polynomial growth, and logarithmic growth).

Continuity as a property of functions
• An intuitive understanding of continuity.  (The function values can be made as
close as desired by taking sufficiently close values of the domain.)
• Understanding continuity in terms of limits.
• Geometric understanding of graphs of continuous functions (Intermediate
Value Theorem and Extreme Value Theorem).

## Collection Contents

by Janet Pinto

Resources in this section listed by standard.
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### LC.1: Understand the concept of limit

by Allen Wolmer

Understand the concept of limit and estimate limits from graphs and tables of values.
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### LC.2: Find limits by substitution.

by Allen Wolmer

Find limits by direct substitution.
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### LC.3: Find limits of sums, differences, products, and quotients.

by Allen Wolmer

Find limits of sums, differences, products, and quotients.
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### LC.4: Find one-sided limits.

by Allen Wolmer

Find one-sided limits.
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### LC.5: Find limits of rational functions that are undefined at a point.

by Allen Wolmer

Find limits of rational functions that are undefined at a point.
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### LC.6: Find limits at infinity.

by Allen Wolmer

Find limits at positive or negative infinity.
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### LC.7: Decide when a limit is infinite.

by Allen Wolmer

Decide when a limit is infinite and use limits involving infinity to describe asymptotic behavior.
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### LC.8: Understand continuity in terms of limits.

by Allen Wolmer

Understand continuity in terms of limits and functional values.
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### LC.9: Decide if a function is continuous at a point.

by Allen Wolmer

Decide if a function is continuous at a point using definition of continuity.
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### LC.10: Find the types of discontinuities of a function.

by Allen Wolmer

Find the types of discontinuities of a function: Removable, Infinite, Jump.
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### LC.11: Understand and use the Intermediate Value Theorem

by Allen Wolmer

Understand and use the Intermediate Value Theorem on a function over a closed interval.
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### LC.12: Understand and apply the Extreme Value Theorem

by Allen Wolmer

Understand and apply the Extreme Value Theorem: If f is continuous over a closed interval, then f has a maximum and a minimum on the interval.
Member Rating
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'C' - Curriki rating

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